Average Error: 3.7 → 0
Time: 1.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(d + a\right) + \left(b + c\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(d + a\right) + \left(b + c\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r76499 = a;
        double r76500 = b;
        double r76501 = c;
        double r76502 = d;
        double r76503 = r76501 + r76502;
        double r76504 = r76500 + r76503;
        double r76505 = r76499 + r76504;
        double r76506 = 2.0;
        double r76507 = r76505 * r76506;
        return r76507;
}
↓
double f(double a, double b, double c, double d) {
        double r76508 = d;
        double r76509 = a;
        double r76510 = r76508 + r76509;
        double r76511 = b;
        double r76512 = c;
        double r76513 = r76511 + r76512;
        double r76514 = r76510 + r76513;
        double r76515 = 2.0;
        double r76516 = r76514 * r76515;
        return r76516;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
  2. Using strategy rm

  3. Applied associate-+r+2.8

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
  4. Using strategy rm

  5. Applied associate-+r+2.8

    \[\leadsto \color{blue}{\left(\left(a + \left(b + c\right)\right) + d\right)} \cdot 2\]
  6. Using strategy rm

  7. Applied +-commutative2.8

    \[\leadsto \color{blue}{\left(d + \left(a + \left(b + c\right)\right)\right)} \cdot 2\]
  8. Using strategy rm

  9. Applied associate-+r+0

    \[\leadsto \color{blue}{\left(\left(d + a\right) + \left(b + c\right)\right)} \cdot 2\]

  10. Final simplification0

    \[\leadsto \left(\left(d + a\right) + \left(b + c\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))